Born in Delft, Osendarp won two bronze medals at the 1936 Summer Olympics in the 100 and 200 m sprint events. The Games being held in Nazi Germany, Osendarp gained some fame as he was the fastest white sprinter, behind the black Americans, of whom Jesse Owens won both events. A possible third medal was lost when Osendarp dropped the baton in the final of the 4 x 100 m relay while fighting for second place.
At the European Championships in 1938, Osendarp won the titles on the 100 m and 200 m, equalling the performance of his compatriot Chris Berger who had accomplished the same feat in 1934.
As a police officer, Osendarp became a member of the German Security Service when Germany occupied the Netherlands in World War II. He later also joined the Dutch national socialist NSB party and the SS.
In 1948, Osendarp was convicted for the acts he committed during the war, although he was released early in 1952. After his release, he moved to Limburg to work in the mines. He died in 2002 in Heerlen.